• READ MORE: Steven Gerrard leads race to become Rangers manager
The 54-year-old has received universal praise since taking over at Kilmarnock earlier this season, moving the Ayrshire side from bottom of the table into fifth place.
Ibrox chiefs sounded out Clarke through a third party over the possibility of replacing Graeme Murty at the end of the season, though the former West Brom and Reading boss wasn’t interested.
Rangers will now turn to other candidates in their search for a manager, with Steven Gerrard the current bookies favourite.
The former Liverpool captain is believed to have held talks with the Ladbrokes Premiership club about taking his first venture into management.